Sam Byrne struck twice inside five first-half minutes before his replacement James Wilson wrapped things up in stoppage time once Pat Roberts had pulled one back for the high-flying Cottagers.
Marek Rodak was tested early on by Jack Barmby, when the United forward fired in a cross-shot from a difficult angle after being fed by Jack Rudge. The Reds continued to look threatening against much-vaunted opponents and Liam Grimshaw was the driving force behind the opener.
The skipper powered out of defence, dribbling past two defenders, before crossing from the right for Joe Rothwell to head goalwards. Rodak did well to paw the effort away but Byrne pounced on the rebound, shooting in off a post.
Barmby was the provider of the second strike, dispossessing Josh Passley to tee up Byrne, who supplied a sweet finish across Rodak to double the lead. Fulham always looked capable of replying, but Barmby and Byrne were unlucky with raking drives at the other end.
Pierluigi Gollini made a couple of smart stops but was powerless to prevent Roberts from scoring in the final seconds of the first half with a perfectly-placed curler following a fine run by George Williams down the right, leaving Barmby in his wake.
Byrne spurned a chance to seal his hat-trick but the hosts had to defend for periods of the second half. Gollini made another top-class stop to thwart Emerson Hyndman and Liam Donnelly headed a chance over the top. Donelly then had another opportunity but Rudge cleared off the line.